The diamond-free process

Details The diamond-free process The diamond-free process

2010-10-25

arxiv.org/abs/1010.5207v1

Mathematics

Combinatorics

25 pages

Scientific paper

Let K_4^- denote the diamond graph, formed by removing an edge from the complete graph K_4. We consider the following random graph process: starting with n isolated vertices, add edges uniformly at random provided no such edge creates a copy of K_4^-. We show that, with probability tending to 1 as $n \to \infty$, the final size of the graph produced is $\Theta(\sqrt{\log(n)} \cdot n^{3/2})$. Our analysis also suggests that the graph produced after i edges are added resembles the random graph, with the additional condition that the edges which do not lie on triangles form a random-looking subgraph.

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